How to get diff to yield result in terms of original function

PS

The gradef approach may also be useful for another reason.  There is no
good representation for the derivative f' of an arbitrary function f in
Maxima.  To represent f'(x), you must use:

    at(diff(f(qqq),qqq),qqq=x)

Note the use of an obscure dummy variable name qqq to avoid substitution
problems.

For this reason, DIFF does not use the chain rule for undefined
functions:

   diff(f(x^2),x) => 'diff(f(x^2),x)

though it could in principle have returned

   2*x*'at(diff(f(qqq),qqq),qqq=x^2))

If you use gradef, on the other hand, you can explicitly define f1, f2,
etc. as the derivatives:

   gradef(f(x),f1(x))
   gradef(f1(x),f2(x))

and now

   diff(f(x^2),x) => 2*x*f1(x^2)
   diff(f(x^2),x,2) => 4*x^2*f2(x^2) + 2*f1(x^2)
   diff(f(f(x)),x,2) => f1(x)^2*f2(f(x)) + f2(x)*f1(f(x))

Unfortunately, Maxima doesn't really know anything about f1, e.g.

   integrate(f1(x),x) => noun

      -s